Given XXX and YYY have joint PDF f(x,y)=4xyf(x, y) = 4xyf(x,y)=4xy for 0≤x,y≤10 \le x, y \le 10≤x,y≤1. Are XXX and YYY independent?
Yes, because the joint PDF factors into g(x)h(y)g(x)h(y)g(x)h(y)
No, because the range is dependent
Yes, because the range is a square
No, because E[XY]≠E[X]E[Y]E[XY] \neq E[X]E[Y]E[XY]=E[X]E[Y]